1. Field of the Invention
This invention relates generally to the field of trapped energy resonators such as those used in piezoeletric crystals. A trapped energy resonator is a piezoelectric resonator which operates in the bulk coupled thickness shear and thickness twist modes. This invention more particularly addresses the problem of placing a number of independent resonators of potentially different resonant frequencies on the same piezoelectric substrate while maintaining acceptable series resistance and minimizing undesired spurious mode activity.
2. Background of the Invention
Several techniques for suppressing undesired spurious mode activity in trapped energy resonators are known in the prior art. By utilizing exotic electrode shapes similar to pie slices and placing barriers between resonators of multi-resonator designs, resonators have been made which improve various types of spurious responses with a limited degree of success. These resonator designs, however, can be implemented only with a sacrifice of other parameters such as series resistance or physical size. Due to the interrelationships of the electrical parameters, they cannot offer the additional degree of design freedom afforded by the present invention. Furthermore, they are often expensive to implement and do not even address the problem of placing a number of resonators of different frequencies on the same substrate. Frequently, the spurious activity they seek to suppress is only filter spurious response caused by undesired coupling between resonators rather than the spurious responses of the individual resonators which is one problem solved by the preferred embodiment of the present invention.
A typical prior art trapped energy resonator is shown in FIG. 1 as resonator 10. In this type of resonator a top metal electrode 15 and a bottom metal electrode 20 are placed on opposite surfaces of a substrate 25 by metal deposition or other process known in the art. The substrate 25 is composed of a piezoelectric material such as quartz which has been cut so that the electrodes will excite the thickness modes, as for example, the AT cut which is well known in the art. In FIG. 1, only one electrode pair is shown, however, the discussions to follow are equally applicable to multi-resonator designs.
A metallized runner 30 is attached to each of the rectangular electrodes 15 and 20 for the purposes of making connections to external circuitry such as an oscillator circuit. For rectangular electrodes such as those shown in FIG. 1, the sides of the electrode are usually disposed along the so-called "X" and "Z" axes of the crystalline structure of substrate 25 as is known in the art. In resonator 10, the series resistance (R.sub.s) of the resonator at resonance is determined essentially by the area of the electrodes.
That is: ##EQU1## where: L.sub.x =the length of the electrode in the "X" direction.
L.sub.z =the length of the electrode in the "Z" direction.
The resonant frequencies of the resonator are characterized by complex equations which are well documented in the art and found in scientific journal articles such as those by H. F. Tiersten entitled "Analysis of Trapped Energy Resonators Operating in Overtones of Coupled Thickness Shear and Thickness Twist" which appeared in the Journal of Acoustic Society of America, Volume 59, No. 4, in April of 1976, and in a commonly authored paper entitled "An Analysis of Overtone Modes in Monolithic Crystal Filters" published in the Proceedinqs of the 30th Annual Symposium on Frequency Control, 1976, Page 103. These articles are hereby incorporated by reference. For the purposes of understanding this invention, however, the resonator's frequency (F) may be closely approximated by the following simple equation which is known in the art and can be derived from the above papers: ##EQU2## H=the sum of the substrate thickness plus the top electrode thickness plus the bottom electrode thickness.
In this equation the various physical constants have been set equal to 1 for convenience. Therefore, equation (2) will not accurately predict the frequency F but it does correctly show the interrelationship between H, L.sub.x, and L.sub.z in determining F.
For substantially rectangular electrodes such as those shown in resonator 10, it is known that spurious mode responses for the series resistance of an individual resonator are optimally minimized when the peripheral geometry of the electrodes is approximately square for an aspect ratio of 1, that is L.sub.x =L.sub.z. This is also a known approximation which is readily derived from the discussion in the above-mentioned papers. The above approximation for frequency (F), equation (2), is correct within a few percent and is sufficiently close for the purposes of understanding the prior art and the present invention so that we may assume a square electrode geometry is the design goal.
It is known that the series resistance (R.sub.s) of a resonator with rectangular electrodes at the spur frequency closest to resonance will typically follow one of the response curves as shown in FIG. 2. FIG. 2 represents the series resistance (or motional inductance) of a resonator as a function of the aspect ratio L.sub.x /L.sub.z of the particular electrode design. Curve 35 shows an increase in R.sub.s with increasing aspect ratio and curve 40 shows a decreases R.sub.s with increasing aspect ratio. The important consideration however, is that both curves maximize near an aspect ratio of one. Therefore, the series resistance of the resonator, at its closest spurious frequencies, is maximum near an electrode aspect ratio of one.
Consider now the problem of placing several resonators of different frequencies on a single substrate using only techniques known in the prior art. This situation is encountered in, for example, a highly miniaturized superheterodyne receiver which, due to size constraints, requires a crystal filter and an oscillator resonator to be placed on the same quartz substrate. Practical fabrication and cost considerations dictate that H must be the same for all of the resonators on the common substrate. Practical circuit considerations normally result in a restriction on the maximum value of R.sub.s which means a minimum electrode area for each resonator. A third normal design constraint is that spurious responses, especially the closest spurs to resonance, be minimized. This implies that L.sub.x should approximately equal L.sub.z.
In this situation, if the required resonant frequency is too high or the required series resistance is too low, the resonator designer has no choice but to degrade spurious responses in order to achieve an acceptable compromise of these goals. Therefore, in order to obtain the correct frequency, serious design compromises in series resistance and spurious responses are necessitated.
Some of the circuit problems which can result from high series resistance in crystal resonators are oscillators which fail to oscillate, or require large amounts of current to initiate and maintain oscillation or stop (or never start) oscillating at low temperatures. These problems are especially troublesome for battery powered portable equipment subject to operation over wide temperature ranges.
The problems which result from poor spurious mode response are best understood by observing FIG. 3 which shows an actual response curve 50 of a 150 MHz 5th overtone oscillator crystal designed according to the above-mentioned prior art design constraints and placed on the same substrate with a crystal filter. Curve 50 was generated by driving the resonator with a 50 ohm source and measuring the voltage output of the crystal loaded into a 50 ohm load. The desired response is at approximately 150 MHz measured at the operating overtone and the peak in response at f.sub.s is the closest spur (about 50 kHz away) to the desired response. For this electrode configuration approximately 700 angstroms of aluminum was disposited on each side of the substrate in a 13.times.68 mil rectangle. The shape factor of the available substrate real estate dictated that a square resonator was impossible. The series resistance at resonance is 150 ohms and at the spurious response it is 500 ohms. The relative loss at the spur frequency is only approximately 7 dB lower than the desired response at 150 MHz.
If this resonator were to be used in a oscillator design, it is quite likely the oscillator would oscillate at both the spurious frequency and at 150 MHz. It is also quite possible for the oscillator to jump from 150 MHz to the spur frequency as a result of temperature fluctuations. Such circuit performance would obviously be unacceptable in a superheterodyne receiver, possibly rendering the receiver inoperative. This problem is elegantly solved by utilizing the present invention.
Although somewhat structurally similar to the present invention, monolithic crystal filter devices, such as those shown in U.S. Pat. No. 4,342,014 to Arvanitis which is commonly assigned to the assignee of the present invention, are distinctly different from the present invention. The individual resonators of Arvanitis must cooperate by being acoustically coupled at approximately the same frequency in order for the filter to function as a bandpass filter with a smooth passband response.
The present invention, on the other hand, is directed toward placing a number of resonators, possibly of various substantially different frequencies, on a single substrate and having them operate in a substantially independent manner with distinct and sharp resonant peaks. Preferrably the resonator would find utility as an oscillator resonator. In operation as a filter, the Arvanitis device will exhibit a broad passband and sharp filter skirts as shown in his FIG. 8 as a result of the high degree of interaction of his resonators. This response is obviously excellent for a filter but renders it impractical to use as an oscillator or other device requiring a sharp, distinct peak. The present invention fills this void by providing a resonator with a sharp, distinct response peak which results from the cooperation of a unique single resonator structure. This structure is useful when a new degree of design freedom is desired in a multiple resonator design having a plurality of resonators which must exhibit independent operation.
The features of the invention believed to be novel are set forth with particularity in the appended claims. The invention itself, however, both as to structure, organization and method of operation, together with further objects and advantages thereof, may be best understood by reference to the following description taken in conjunction with the accompanying drawings.